Semiclassical Routes to the $\alpha$-RuCl$_3$ Scattering Continuum via Model Meta$-$Analysis

Abstract

$\alpha$-RuCl$_3$ is a leading material for proximate Kitaev magnetism. We address the origin of the broad, $\Gamma$-point centered excitation continuum observed by inelastic neutron scattering at elevated temperatures in this compound. Using stochastic Landau-Lifshitz dynamics augmented with quantum-equivalent corrections, we reproduce the temperature-dependent dynamical spin structure factor across both the correlated and conventional paramagnetic regimes. A meta-analysis of 38 published exchange parameter sets identifies those most consistent with the full temperature evolution. A Bayesian optimization procedure is used to derive parameters that capture the low-energy star-like momentum dependence and the overall bandwidth of the continuum. Rescaling temperatures by the Curie--Weiss scale produces a collapse of spectral measures, demonstrating that the high-$T$ dynamics are governed by correlated paramagnetism below $\theta_{\mathrm{CW}}$ rather than by the Kitaev crossover to fractionalized excitations. Complementary 24-site exact diagonalization clarifies finite-size systematics at low temperature and the proximity to zigzag/incommensurate ordering. Beyond $\alpha$-RuCl$_3$, our simulation pipeline provides a reproducible, data-driven framework to infer effective spin models in magnets that exhibit broad continua.